Problem: Solve for $x$ and $y$ using elimination. ${3x+5y = 36}$ ${2x+3y = 22}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-2$ and the bottom equation by $3$ ${-6x-10y = -72}$ $6x+9y = 66$ Add the top and bottom equations together. $-y = -6$ $\dfrac{-y}{{-1}} = \dfrac{-6}{{-1}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {3x+5y = 36}\thinspace$ to find $x$ ${3x + 5}{(6)}{= 36}$ $3x+30 = 36$ $3x+30{-30} = 36{-30}$ $3x = 6$ $\dfrac{3x}{{3}} = \dfrac{6}{{3}}$ ${x = 2}$ You can also plug ${y = 6}$ into $\thinspace {2x+3y = 22}\thinspace$ and get the same answer for $x$ : ${2x + 3}{(6)}{= 22}$ ${x = 2}$